1 Getting started

 

This chapter covers

  • Definition of applied geometry and its relations to mathematics, engineering, and computer science
  • Which programming domains rely on geometry
  • The reason to start learning applied geometry today
  • What do you need to know to get started
  • Making SymPy do the math for you

Applied geometry is the geometry people make money with. It stands behind game engines, computer-aided design applications, 3D printing platforms, image processing libraries, and geographic information systems. As soon as there are curves, surfaces, or spaces, there is applied geometry involved.

Normally, you don’t have to be a geometer to use an application with curves and surfaces. Don’t worry, this book will not convert you into one. However, just as knowing the mechanics behind your car allows you to make the most of driving it, knowing the mathematics behind your tools will allow you to use them in the most efficient way possible.

For instance, to programmatically 3D-print an engine spare part, or prosthetic hip joint, or just a toy figurine you need to convert the model from smooth surfaces to triangles with a special library, then ensure that the triangulated model is printable with an analysis algorithm, then turn the model into a list of contours with a slicing function, and only then you can start an actual printing machine. Each part of the process before clicking a switch is applied geometry wrapped in programming (figure 1.1).

1.1 What is applied geometry?

1.2 Which programming domains require geometry?

1.3 Why not let my tools take care of geometry?

1.4 Applied geometry has been there forever, why learn it now?

1.5 It is not a lot to know to get started

1.6 Meet SymPy, it will do your math for you

1.7 Summary